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Exact Bayesian regression of piecewise constant functions

Hutter, Marcus

Description

We derive an exact and ecient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary locations, and levels. The derivation works for any noise and segment level prior, e.g. Cauchy which can handle outliers. We derive simple but good estimates for the in-segment variance. We also propose a Bayesian regression curve as a better way of smoothing data without blurring boundaries. The Bayesian approach also allows straightforward determination of the...[Show more]

dc.contributor.authorHutter, Marcus
dc.date.accessioned2015-12-10T22:15:46Z
dc.identifier.issn1931-6690
dc.identifier.urihttp://hdl.handle.net/1885/50847
dc.description.abstractWe derive an exact and ecient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary locations, and levels. The derivation works for any noise and segment level prior, e.g. Cauchy which can handle outliers. We derive simple but good estimates for the in-segment variance. We also propose a Bayesian regression curve as a better way of smoothing data without blurring boundaries. The Bayesian approach also allows straightforward determination of the evidence, break probabilities and error estimates, useful for model selection and signicance and robustness studies. We discuss the performance on synthetic and real-world examples. Many possible extensions are discussed.
dc.publisherCarnegie Mellon University
dc.rightsCopyright Information: © 2007 International Society for Bayesian Analysis. http://www.sherpa.ac.uk/romeo/issn/1936-0975/..."Publisher's version/PDF may be used. on author's personal website or any other website" from SHERPA/RoMEO site (as at 27/08/15)
dc.sourceBayesian Analysis
dc.subjectKeywords: Bayesian regression; Change point problem.; Dynamic programming; Exact polynomial algorithm; Non-parametric inference; Piecewise constant function
dc.titleExact Bayesian regression of piecewise constant functions
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume2
dc.date.issued2007
local.identifier.absfor010405 - Statistical Theory
local.identifier.absfor080199 - Artificial Intelligence and Image Processing not elsewhere classified
local.identifier.absfor080401 - Coding and Information Theory
local.identifier.ariespublicationu8803936xPUB211
local.type.statusPublished Version
local.contributor.affiliationHutter, Marcus, College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage635
local.bibliographicCitation.lastpage664
local.identifier.doi10.1214/07-BA225
dc.date.updated2016-02-24T11:43:38Z
local.identifier.scopusID2-s2.0-65449146082
CollectionsANU Research Publications

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